Rehearsals for Fela, which opens next month at the National Theatre. The redevelopment aims to open backstage areas to the public. Photograph: Tristram Kenton

The businessman Lloyd Dorfman has given the National Theatre £10m – its biggest ever private donation – which will go towards the organisation's ambitious £70m redevelopment, it was announcedtoday.

To recognise the gift, the Cottesloe theatre will be renamed the Dorfman theatre when it reopens in 2013.

Dorfman is the founder and chairman of Travelex, a business he built up from a small shop in central London 34 years ago into what is now the world's largest foreign exchange specialist. For the last eight years, Travelex has sponsored the NT's successful £10 ticket scheme.

Nicholas Hytner, the NT's director, said the £10 scheme had been emblematic of a new kind of National Theatre and Dorfman's "far-sighted spirit and vision" were a perfect match for it.

"But I never dreamt that his involvement with the National would have such a far-reaching and transformational effect. I couldn't be more grateful to him; it is entirely fitting that his family name will be associated with an auditorium which often plays host to our most innovative work, and whose redevelopment will transform our facilities to introduce theatre to generations to come."

The redevelopment aims to open up Denys Lasdun's love-it-or-hate-it building on London's South Bank.

Lambeth council last month granted planning permission for the work, which the National hopes to begin in spring 2012 and complete by the end of 2014.

Among the aims of the plan, called NT Future, are:

•To create a new education and participation "Discover" centre allowing in an extra 50,000 people a year;

• To redevelop the Cottesloe – the smallest of the National's three spaces which presently seats 300-400 depending on the production – into a more comfortable theatre with better access;

•To open up the NT building to enable audiences to see its internal life and theatre-making processes, with a high-level public walkway through workshops and backstage areas; and

• To relieve the pressure on what are often chock-a-block foyers and open a new cafe-bar on the north-east riverfront corner where the waste and goods facilities are.

Such philanthropy will be music to the ears of the culture secretary, Jeremy Hunt, who hopes to encourage this type of giving. Alan Davey, the chief executive of Arts Council England, is preparing a reportfor Hunt on private donations to the arts, which is due in a few weeks.

Hayden Phillips, the chairman of the National Theatre, said Dorfman's "supremely generous gift … will further the National's determination and ability to thrive in the coming years. I hope it will act as a spur and inspiration to other philanthropists, as a powerful demonstration of faith in the arts."

The Cottesloe was originally named after Lord Cottesloe, who was chairman of the South Bank board which oversaw the building of the National Theatre.

His name will live on in an adjoining public room to the Dorfman, called the Cottesloe Room.

If all goes to plan, the Cottesloe will close for nine months and reopen as the Dorfman in autumn 2013.

Dorfman said: "I am a huge fan of the energy and innovation the National has achieved in recent years and am delighted to lead from the front in supporting its NT Future redevelopment.

"Individual and corporate support is vital to building on London's leadership in the arts and I hope others will join me in wanting to build on the National's role at the heart of modern theatre and sustaining it long into the future."